Propositions, Properties and Paradox

Abstract

Contrary to views that diagnose the paradoxes of truth and related notions in terms of sentences not expressing propositions, or expressing propositions different from what they appear to express and which aren’t paradoxical, or expressing multiple propositions none of which are paradoxical, the paper argues that the basic paradoxes are paradoxes of propositions; or alternatively, of sentential quantification. Similarly for the paradoxes of satisfaction: the basic paradoxes arise for properties, or for quantification into predicate position. (In the latter case, it’s argued that adopting the syntactic restrictions of Russellian type theory is not the best way to go.). The paradoxes of propositions and properties can be resolved either in classical or non-classical logic, but the paper focuses mostly on non-classical options, and develops an account of property identity in which properties defined using the notion of property identity are allowed and the naive abstraction principle holds unrestrictedly.